Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Solution {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        // n = (a(a+1) + b(b+1)) / 2
        for (int i = 1; (i*(i+1)) <= n; i++) {
            int t1 = (i*(i+1)) / 2;

            if (isTriangle(n - t1)) {
                System.out.println("YES");
                return;
            }
        }

        System.out.println("NO");
    }
    
    public static boolean isTriangle(int num) {
        // 2*num = (a*(a+1))
        num *= 2;

        int root = (int) Math.sqrt(num);

        for (int i = root; (i*(i+1)) <= num; i++) {
            int candidate = i * (i + 1);

            if (candidate == num) {
                return true;
            }
        }

        return false;
    }
}